1. Bond Portfolio

2. Issuers, Investors & important features
Issuers – Central Govt., State Govt., PSUS, Corporate Bodies, Banks.
Investors – Banks, Insurance Companies, PFs, Individuals, Trusts, corporate bodies
Law requires that certain categories must invest in debt securities. Like Banks must invest at least 25% of demand and time deposits in the T-Bills, Central Govt. Bonds and state Govt. development loans and other approved securities (SLR requirement)
Corporate bonds require ratings
Maturity of Central Govt. bonds extend up to 30 years.
Debt securities issued by the Central Govt. (G-Sec) are considered risk-free. In the jargon of credit rating agencies they are supposed to be AAA+, the plus (+) comes from right to print currency notes.
All bonds other than G-sec bonds carry credit risk. Even Industrial Finance Corporation of India Ltd defaulted.
In most bond markets clearing and settlement are done by specialized clearing companies. In India the function is discharged by the Clearing Corporation of India Ltd. (CCIL)

3. Determinants of Bond Safety
Almost similar credit analysis carried out by the banks and Financial Institutions.
Coverage Ratio ( Interest Coverage Ratio = EBIT/ I, EBITDA/ I, Cash Flow Coverage Ratio =EBIDTA / Interest on debt + Loan Repayment Installment/ (1- tax rate) etc.
Leverage Ratio
Profitability Ratios
Liquidity Ratios

4. Bond - Basics Bond (option free) Callable Bond Puttable Bond
Yield (Current) [coupon interest/current Price] ( T-bills are zero coupon bonds. A 91 day T-bill priced, at say Rs will thus yield -1.50/98.50 X 365/91=6.108% p.a.)
Yield to Maturity (YTM) [ =IRR, Different from current yield]
Floating Rate Bond
Junk Bond (Low-rated bonds. In India mostly junk bonds are ‘fallen angels’)
Zero coupon Bond (Deep Discounts Bond)
Premium bond ( selling over par value, coupon > current yield)
Discount Bond ( selling below par value, coupon < current yield)
Clean Price / Dirty Price.
Commercial Papers (issued by corporate houses for raising short term fund – requires rating, may be issued at a discount to face value)
Certificate of Deposits (Like CP issued except that issuer is bank)

5. Reasons for Change in the Price of a Bond
Change in the credit quality of the issuer
Change in the required yield of a comparable bond.
Movement towards maturity of a discount / premium bond.
Note: Bond prices approach par value as maturity approaches.

6. Credit Risk Bond Investors are exposed to the following Risks:
Default Risk : Normally for Corporate Bonds, not for Govt. Bonds. Govt. bonds are considered default-free.
Credit Spread risk: Generally arises from required yield of the economy.
Yield is made up of :
a) yield on a similar default-free bond issue
b) a premium over the yield of default-free bond necessary to
compensate for the risk associated with the bond.
The risk premium is referred to as a yield spread. The part of the risk premium attributable to default risk is called the ‘credit spread’. If the spread has “widened” the market price will decline.
3. Downgrade Risk: high grade means low credit risk, low grade means high risk. Downgrading is closely associated with high credit spread risk.

7. Dynamic Price-Yield Relationship for Option – Free Bond
Bond Prices and Yields are inversely related, as yields increase bond prices fall and vice versa
An increase in a bond’s yield to maturity results in a smaller price change than a decrease in yield of equal magnitude.
Putting differently -
The shape of the price-yield relationship is referred to as convex – meaning decrease in yield have bigger impact on prices than increases in yields of equal magnitude
Prices of long term bonds tend to be more sensitive to interest rate changes than the prices of short tem bond. Thus, prices of long term bond is more volatile.
The sensitivity of a bond’s price to a change in yield increases at a decreasing rate as maturity increases. Thus, interest rate sensitivity increases with maturity but it does so less than proportionally as bond maturity increases.
Interest rate risk is inversely related to the bond’s coupon rate. Prices of high coupon bonds are less sensitive to changes in the interest rate than the prices of low- coupon bond
The sensitivity of a bond’s price to a change in its yield is inversely related to yield to maturity at which the bond is currently trading.

8. Change in bond price as a function of change in YTM
Bond Face Value Coupon Maturity YTM Price current Y % Change in Price
X % year %
A % year % %
B % year % %
C % years % %
D % years % %
E % year % %
F % year
G % year

9. Summary on Sensitivity
The relation between interest rate and bond price enumerated in slide 7 (rule 1 to 5) and illustrated in slide 8 characterize sensitivity of bond price to interest rate. Putting in a different way we can summarize our findings as under:
Although the price moves in the opposite direction from the change in yield, % price change is not the same for all bonds.
For a small change in yield, % price change for a given bond is roughly the same, whether the yield increases or decreases.
For large changes in yield, % change is not the same for an increase in yield as it is for decrease.
For a given large changes in the yield, % price increase of a bond > % price decrease. The capital gain realized from decrease in yield > capital loss generating from increase in yield for the same number of basis points.
The sensitivity of a bond’s price to change in market interest rate (current yield) is influenced by 3 key factors, namely :
Time to maturity
Coupon rate, and
YTM

10. Duration
Currently a bond is selling at Rs.90 to a yield of 6%. Suppose interest rate increases by 25 basis points to become 6.25%. Now, it requires a valuation model to assess the price. Let us say price becomes Rs. 88 to 6.25% yield. i.e. price decline is 2.22% of the initial price. If 2.22% is divided by 25 basis points the price decline is % per 1 basis point change in yield
If yield declines from 6% to 5.75%, the price increase is by Rs.2.70 i.e. 3.00% on Rs. 90. price change is % per 1 basis point change in yield.
Average change is ( ) / 2 = % . This means for a 100 basis point change (i.e.1%) in yield, the average % price change is 10.44%.
A formula for approximate % price change for a 100 basis point change in yield
price if yields decline – price if yields rise
2 x (initial price) x( change in yield in decimal)
The estimated price change for a 100 basis point change in yield is called duration.
Thus duration is a measure of the price sensitivity of a bond to a change in yield.

11. Price Volatility with Embedded option
Callable Bond: Price/ yield relationship between Option –free bond and a callable bond will not be very different
1) when coupon rate < current yield, as in such case the issuer is unlikely to exercise option.
Price of a callable bond = Price of an option free bond of the identical maturity + Price of the option. If coupon rate is 7 % and yield is 8%, issuer is unlikely to exercise the option. As yield comes down, probability of option exercise increases. At low yield level the value of embedded call option is high. Unlike option free bond, its price appreciation is less than its price decline when yield changes by a large basis point – referred to as ‘negative convexity’. Price/yield carve shows a negative convexity at low yield level and a positive convexity at high yield level.
Putable Bonds: May be redeemed by the investors on specified date /dates at the put option price. If the yield > coupon rate the investors will exercise the put option. Value of put option = value of option free bond + value of the option.
At low level of yield (compared to coupon rate) the price of putable bond remains basically at the same level as option-free bond, but as yield rises the price of bond declines but not at the same rate as option free bond

12. Macaulay’s Duration and Implication
Macaulay’s duration is computed by dividing the weighted average of PV of each coupon ( & principal) payment made by the bond by price. The weight associated with each payment is the product of Time and PV of each coupon and principal divided by the bond price.
Investors refer Modified Duration (D) as under :
Macaulay duration (D)/ 1+y
Again, dp 1 = - modified duration, alternatively ∆P/P = -D x ∆y
dy P
Duration is a key concept of the fixed income portfolio management:
It is a summary statistics of the effective average maturity of the portfolio.
It is an essential tool in immunizing portfolios from interest rate risk
Is a measure of interest rate sensitivity
Long term bonds are more sensitive to interest rate movements than short term bonds. Duration measure enables to quantify the relationship.

13. Rules of Duration
The duration of zero coupon bond equals its time to maturity
Holding Maturity constant a bond’s duration is higher when coupon rate is lower.
Holding the coupon rate constant bond’s duration generally increases with its time to maturity. Duration always increases with maturity of bonds selling at par or at a premium to par
Holding other factors constant duration of a coupon bond is higher when the bond’s YTM is lower.
Duration of a perpetuity 1+y/y ( At 10 % yield, the duration of a perpetuity that gives Rs.100 = 1.10/0.10 =11years. At 8% yield it is 1.08/.08 = 13.5 years. The relation shows that maturity and duration may vary substantially. Here in both the cases maturity is infinite but duration is finite, 11 and 13.5 years respectively)